To remove large particulates not strongly bonded to the surface, a surfactant (like soap or Tergitol) in DI water with ultrasonic agitation is effective at removing this type of dirt. Follow with running DI rinse.

Solvent with Ultrasound:

For some larger particles/organic residues, ultrasonic agitation in a solvent such as Acetone can work.

Wet Etchants:

Some particulates can be effectively oxidized and removed by strong oxidizers.